If they put their drink in THEIR left hand holder, it wouldn't be near you, so why 'put out'?
If they put it in their right hand holder, you could politely ask them to move it, if you feel so 'put out'.
Bear in mind it's public property, so anybody can use any side they wish to; you don't 'own' the left hand one!

Your lucky! The theatre we always go too, doesn't have drink holders! I've how forgotten who wrote that they were left-handed. Our 2 young grand-daughters are both left-handed! Is that because the younger 1 copied what her older sister was doing when she was learning to draw? She's nearly 3 &1/4 years old.

Yes, Sandy, believe there is. Think at the Theatre, starts counting from the right, as you look at the stage. So that would be the right armrest all the way. The lucky person at the left end gets two!
Just at a concert this arvo, had woman to my right wanting to take 'all' of my right (her left) armrest. I explained the 'protocol' to her & she moved her arm.
Interesting if get a left handed person! Hopefully it gets sorted!

Whichever one is not being used!!! Or the one which is between me and my special friend if I have gone with him!! I rarely even go to cinemas any more as I find sitting too long is very difficult for me nowadays!

They both are. The person with the shortest arms has the half closest to back rest, and person with longest arms has the front half. Or...lift the arm rest up and cuddle the beautiful person beside you.